Vibration Resistant Cable

ABSTRACT

A vibration resistant cable may be provided. The vibration resistant cable may comprise a first conductor and a second conductor. The first conductor and the second conductor may each have a diameter d. The second conductor may be twisted around the first conductor at a lay length determined as a function of the diameter d and may be configured to reduce relative movement of the first conductor and the second conductor that would result in bags in the vibration resistant cable.

REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of co-pending U.S. patentapplication Ser. No. 13/245,150, filed on Sep. 26, 2011, now U.S. Pat.No. 8,624,110, which is continuation application of U.S. patentapplication Ser. No. 12/885,604, filed on Sep. 20, 2010, now abandoned,which is a continuation application of U.S. patent application Ser. No.12/177,945, filed on Jul. 23, 2008, now U.S. Pat. No. 7,807,922, whichclaims the benefit of U.S. Provisional Application No. 60/952,692, filedon Jul. 30, 2007, U.S. Provisional Application No. 61/022,630, filed onJan. 22, 2008, and U.S. Provisional Application No. 61/061,168, filed onJun. 13, 2008, all of which are incorporated herein by reference intheir entirety.

COPYRIGHTS

All rights, including copyrights, in the material included herein arevested in and the property of the Applicant. The Applicant retains andreserve all rights in the material included herein, and grant permissionto reproduce the material only in connection with reproduction of thegranted patent and for no other purpose.

BACKGROUND

Electrical energy is transmitted using power lines. Power lines includeelectrical conductors configured to conduct the electrical energy. Theelectrical conductors are supported or suspended from power linestructures similar to a power line structure 100 as described below withresects to FIG. 1A. Because power lines are exposed to meteorologicalelements, power lines may be designed and constructed to withstandpotential damages that may be caused by vibrations due to meteorologicalelements such as wind and/or ice, for example. Due to meteorologicalelements, a number of undesirable vibration phenomenon may occur, forexample, “aeolian” vibration (e.g. torsional conductor movement andstring vibration) which can lead to conductor fatigue failures andconductor “galloping.” These undesirable vibration phenomenon may resultin: i) contact between multiple conductors or between multipleconductors and overhead ground wires (i.e. shields); ii) conductorfailure at support points on power line structures due to vibrationinduced stress; iii) possible power line structure damage; and iv)excessive conductor sag due to conductor overstressing.

Aeolian vibration is a high-frequency low-amplitude oscillationgenerated by a low velocity, comparatively steady wind blowing across aconductor. This steady wind creates air vortices or eddies on the leeside of the conductor. These vortices or eddies will detach at regularintervals from the top and bottom area of the conductor (i.e. “vortexshedding”) creating a force on the conductor that is alternatelyimpressed from above and below. If the frequency of the forces (i.e.expected excitation frequency) approximately corresponds to a frequencyof a resonant vibration mode for a conductor span (i.e. naturalfrequency of the power line), the conductor will tend to vibrate in manyloops in a vertical plane. The frequency of resonant vibration dependsmainly on conductor size and wind velocity and is generally between 5and 100 Hz for wind speeds within the range of 0 to 15 miles per hour.The peak-to-peak vibration amplitudes will cause alternating bendingstresses great enough to produce fatigue failure in the conductorstrands at the attachment points to the power line structure. Highlytensioned conductors in long spans are particularly subject to vibrationfatigue. This vibration is generally more severe in flat open terrainwhere steady winds are more often encountered.

Conductor galloping (sometimes called dancing), is a phenomenon wherepower line conductors move or vibrate with large amplitudes. Gallopingusually occurs when an unsteady, high or gusty wind blows over aconductor covered by a layer of ice deposited by freezing rain, mist, orsleet. The coating may vary from a very thin glaze on one side to asolid three-inch cover giving the conductor an irregularly shapedprofile. Consequently, this ice covering may give the conductor aslightly out-of-round, elliptical, or quasi-airfoil shape. Wind blowingover this irregularly shaped profile results in aerodynamic lift thatcauses the conductor to gallop. The wind can be anything between 5 to 45miles-per-hour at an angle to the power line of 10 to 90 degrees. Thewind may be unsteady in velocity or direction.

During galloping, conductors oscillate elliptically at frequencies onthe order of 1-Hz or less with vertical amplitudes of several feet.Sometimes two loops appear, superimposed on one basic loop. Single-loopgalloping rarely occurs in spans over 600 to 700 feet. This is fortunatebecause it would be impractical to provide clearances large enough inlong spans to prevent the possibility of contact between phases. Indouble-loop galloping, the maximum amplitude usually occurs at thequarter span points and is smaller than that resulting from single-loopgalloping. There are several measures that can be incorporated at thepower line's design stage to reduce potential conductor contacts causedby galloping, such as designing the power line to have shorter spans, orincreased phase separation.

In areas where galloping is either historically known to occur or isexpected, power line designers should indicate design measures that willminimize galloping and galloping problems, especially conductorcontacts. The primary tool for assuring absence of conductor contacts isto superimpose Lissajous ellipses over a structure's scaled diagram toindicate a galloping conductor's theoretical path. FIG. 1A shows powerline structure 100, a first phase Lissajous ellipse 105, a second phaseLissajous ellipse 110, a third phase Lissajous ellipse 115, a firstshield Lissajous ellipse 120, and a second shield Lissajous ellipse 125.Ways to calculate the aforementioned Lissajous ellipses is shown inTable 1 and FIG. 1B.

TABLE 1 Single Loop Double Loop Major Axis ‘M’ M = 1.25 S_(i) + 1.0 Eq.6-7 $\quad\begin{matrix}{\quad{\quad{M = {1.0 + \sqrt{\frac{3{a\left( {L + \frac{8S_{i}^{2}}{3L} - {2a}} \right)}}{8}}}}}} \\{{{where}\mspace{14mu} a} = \sqrt{\left( \frac{L}{2} \right)^{2} + S_{i}^{2}}}\end{matrix}$ Eq. 6-8 Distance‘B’ B = 0.25 S_(i) Eq. 6-9 B = 0.2M Eq.6-10 Minor Axis ‘D’ D = 0.4M Eq. 6-11 D = 2{square root over (M − 1.0)}Eq. 6-12 Where: p_(c) = wind load per unit length on iced conductor inlbs/ft. Assume a 2 psf wind. w_(c) = weight per unit length of conductorplus 1/2 in. of radial ice, lbs/ft L = span length in feet. M = majoraxis of Lissajous ellipses in feet. S_(i) = final sag of conductor with1/2 in. of radial ice, no wind, at 32° F., in feet. D = minor axis ofLissajous ellipses in feet. B,  = as defined in figure above

To avoid contact between phase conductors or between phase conductorsand shield wires, none of the ellipses (i.e. first phase Lissajousellipse 105, second phase Lissajous ellipse 110, third phase Lissajousellipse 115, first shield Lissajous ellipse 120, and second shieldLissajous ellipse 125) should touch one another. However, if gallopingis expected to be infrequent and of minimal severity, there may besituations where allowing ellipses to overlap may be the favored designchoice when economics are considered.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter. Nor is this Summaryintended to be used to limit the claimed subject matter's scope.

A vibration resistant cable may be provided. The vibration resistantcable may comprise a first conductor and a second conductor. The secondconductor may be twisted around the first conductor at a lay lengthconfigured to cause a locking force between the first conductor and thesecond conductor. The locking force may be configured to preventrelative movement of the first conductor and the second conductor thatmay result in bags in the vibration resistant cable.

Both the foregoing general description and the following detaileddescription provide examples and are explanatory only. Accordingly, theforegoing general description and the following detailed descriptionshould not be considered to be restrictive. Further, features orvariations may be provided in addition to those set forth herein. Forexample, embodiments may be directed to various feature combinations andsub-combinations described in the detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this disclosure, illustrate various embodiments of the presentinvention. In the drawings:

FIG. 1A is a diagram illustrating conductor galloping;

FIG. 1B is a diagram illustrating ways to calculate Lissajous ellipses;

FIG. 2 is a diagram showing a vibration resistant cable;

FIG. 3A illustrates a “swallow” VR cable;

FIG. 3B, shows a VR cable comprising two individual conductors twistedtogether;

FIG. 4A shows a 3 ft. lay length VR cable;

FIG. 4B shows a 9 ft. lay length VR cable;

FIG. 4C shows a combination 6 ft. and 3 ft. lay length VR cable;

FIG. 5A shows an overall mesh;

FIG. 5B shows a close-up VR cable and mesh;

FIG. 6A is a key for the directions;

FIG. 6B shows the directions of the simulated unsteady flow behavior ofair at 25 mph over the VR cable;

FIG. 7 shows the VR lay configuration plane locations;

FIGS. 8A, 8B, and 8C show flow velocity of the 3 ft. lay VR cable atplane 1, plane 2, and plane 3 respectively;

FIGS. 9A, 9B, and 9C show pressure of the 3 ft. lay VR cable at plane 1,plane 2, and plane 3 respectively;

FIGS. 10A, 10B, and 100 show flow velocity at various times of the 3 ft.lay VR cable at plane 2;

FIGS. 11A, 11B, and 11C show flow pressure at various times of the 3 ft.lay VR cable at plane 2;

FIGS. 12A, 12B, and 12C show forces on the 3 ft. lay VR cable at plane1, plane 2, and plane 3 respectively;

FIGS. 13A, 13B, and 13C show flow velocity of the 9 ft. lay VR cable atplane 1, plane 2, and plane 3 respectively;

FIGS. 14A, 14B, and 14C show pressure of the 9 ft. lay VR cable at plane1, plane 2, and plane 3 respectively;

FIGS. 15A, 15B, and 15C show flow velocity at various times of the 9 ft.lay VR cable at plane 2;

FIGS. 16A, 16B, and 16C show flow pressure at various times of the 9 ft.lay VR cable at plane 2;

FIGS. 17A, 17B, and 17C show forces on the 9 ft. lay VR cable at plane1, plane 2, and plane 3 respectively;

FIGS. 18A, 18B, and 18C show flow velocity of the 6 ft.-3 ft.combination lay VR cable at plane 1, plane 2, and plane 3 respectively;

FIGS. 19A, 19B, and 19C show pressure of the 6 ft.-3 ft. combination layVR cable at plane 1, plane 2, and plane 3 respectively;

FIGS. 20A, 20B, and 20C show flow velocity at various times of the 6ft.-3 ft. combination lay VR cable at plane 2;

FIGS. 21A, 21B, and 21C show flow pressure at various times of the 6ft.-3 ft. combination lay VR cable at plane 2;

FIGS. 22A, 22B, and 22C show forces on the 6 ft.-3 ft. combination layVR cable at plane 1, plane 2, and plane 3 respectively;

FIG. 23 shows the detailed examination for the 9 ft. lay VR cable (e.g.FIG. 4B);

FIG. 24 shows the detailed examination for a 3 ft. lay VR cable (e.g.FIG. 4A.);

FIG. 25 illustrates a 3 ft. long section of a 1 ft. lay VR cable;

FIG. 26A shows flow pressure at a time of the 1 ft. lay VR cable at midspan plane;

FIG. 26B is a corresponding force plot with respect to time;

FIG. 27A shows velocity vectors plotted near the surface of the 3 ft.lay VR cable;

FIG. 27B shows velocity vectors with span-wise speed; and

FIG. 28 shows the span-wise flow directed towards the cross-section thatsubtends the smallest area to the incoming flow.

DETAILED DESCRIPTION

The following detailed description refers to the accompanying drawings.Wherever possible, the same reference numbers are used in the drawingsand the following description to refer to the same or similar elements.While embodiments of the invention may be described, modifications,adaptations, and other implementations are possible. For example,substitutions, additions, or modifications may be made to the elementsillustrated in the drawings, and the methods described herein may bemodified by substituting, reordering, or adding stages to the disclosedmethods. Accordingly, the following detailed description does not limitthe invention.

A vibration resistant (VR) cable may be provided. Consistent withembodiments of the invention, the VR cable may comprise a firstconductor twisted around a second conductor at a predetermined orvarying lay length. Consequently, embodiments of the invention mayprovide a changing profile to wind due to the VR cable's twisting naturethat may prevent excitation in a vibration mode with or without icebuildup when the VR cable is used in a power line. Embodiments of theinvention may change the twisting angle and or lay length of the twoconductors such that more twists occur in a given length than inconventional systems. In other words, embodiments of the invention mayhave shorter lay lengths than conventional systems. Computational FluidDynamics may be used as a tool to demonstrate embodiments consistentwith the invention.

In conventional systems, long lay lengths cause unwanted relativemovement of the two conductors during manufacturing or installation thatcreate “bags” (e.g. “loops”) in the cable. These bags cause conductorscomprising the cable not to stay together as one profile and are thusundesirable. These bags may occur during construction of a power lineusing the cable, after the power line using the cable is constructed, oreven during manufacture of the cable. In addition, it is time consumingand expensive to correct these conditions after they occur. Consistentwith embodiments of the invention, shorter lay lengths may help holdconductors together better in the VR cable. Moreover, the shorter laylengths may aid in manufacturing and installation by preventing unwantedrelative movement of the two conductors during manufacturing orinstallation that create bags.

Furthermore, the lay length may be chosen (e.g. when applied in a powerline) to set the VR cable's natural frequency to lessen or avoidgalloping modes and aeolian vibration modes (i.e. torsional modes and“string” type vibration modes.) Embodiment of the invention may providepower lines with natural frequencies that may be less likely to beexcited by, for example, wind blowing across the power lines' cables.This may be true in conditions when the cable is covered with ice andwhen it is not. Consistent with embodiments of the invention, cableshaving shorter lay lengths or a lay lengths that may vary may be a less“excitable” by winds having a frequency and speeds expected to blow onthe cable. Moreover, a tighter lay length (i.e. more twists per unitlength) may change the stiffness and damping of the VR cable to dampenvibrations that may develop before the vibrations produce damage to theVR cable.

FIG. 2 shows a VR cable 200 consistent with embodiments of theinvention. As shown in FIG. 2, VR cable 200 may comprise a firstconductor 205 and a second conductor 210 twisted around one another.Cable 200 may have a lay length X. Lay length X may be constant over aunit length of VR cable 200 or may vary over a unit length of VR cable200. For example, lay length X may vary at a constant rate between twofeet and four feet for every fifty feet of VR cable 200. Moreover, laylength X may vary at a non-constant rate. Elements 215 a through 215 jshow cross sections of VR cable 200 at their respective correspondinglocations. For example, between elements 215 c and 215 h, one twist ofVR cable 200 corresponding to lay length X may occur. VR cable 200 maybe used in any power line. RUS BULLETIN 1724E-200, “DESIGN MANUAL FORHIGH VOLTAGE TRANSMISSION LINES”, published by the Electric StaffDivision, Rural Utilities Service, U.S. Department of Agriculture showshow power lines may be designed and is incorporated herein by reference.

Lay length X may be configured to cause a power line using VR cable 200to have a natural frequency not equal to an expected excitationfrequency for an environment in which the power line is constructed.Moreover, the natural frequency may not only be unequal to the expectedexcitation frequency, but the natural frequency may be made sufficientlydifferent than the expected excitation frequency by a predeterminedvalue. In other words, the difference between the natural frequency andthe expected excitation frequency may be different by a value that maybe predetermined. Furthermore, a power line using VR cable 200 with laylength X may be determined to have a natural frequency range. Likewise,the expected excitation frequency for the environment in which the powerline is constructed may have a range. Consistent with embodiments of theinvention, lay length X may have a value configured to cause theaforementioned natural frequency range and the aforementioned expectedexcitation frequency range to not overlap or to have a buffer frequencyrange between the aforementioned natural frequency range and theaforementioned expected excitation frequency range.

For example, a frequency of a resonant vibration mode for a span in thepower line may comprise the natural frequency. The natural frequency maydepend on conductor size (e.g. diameter, weight, etc.) and wind velocityand is generally between 5 and 100 Hz for wind speeds within the rangeof 0 to 15 miles per hour. The expected excitation frequency maycomprise the frequency of the forces (e.g. wind) acting upon the powerline. Consistent with embodiments of the invention, lay length X may beconstant over a unit length of VR cable 200 or may vary over a unitlength of VR cable 200. Lay length X may be selected to cause the powerline to have a natural frequency not equal to the expected excitationfrequency for the environment in which the power line is constructed. Inthis way, because the natural frequency may not be equal to the expectedexcitation frequency, wind corresponding to the expected excitationfrequency may: i) not be able to cause a vibration phenomenon in VRcable 200 used in the power line or ii) may only cause a minimalvibration phenomenon in VR cable 200 that may not damage the power line.

In addition, lay length X may be configured to cause a power line usingVR cable 200 to provide a dampening effect to the power line using VRcable 200 to vibration phenomenon caused at the expected excitationfrequency for an environment in which the power line is constructed.Consistent with embodiments of the invention, lay length X may beselected to cause VR cable 200 to be less “excitable” by winds having afrequency and speeds expected to blow on VR cable 200 used in the powerline. In other words, “excitation characteristics” for VR cable 200 maybe selected in such a way that energy from wind may be dampened evenwhen the natural frequency range for the power line may overlap theexpected excitation frequency range of the power line's expectedenvironment. The excitation characteristics may be selected to cause theaforementioned dampening effect by selecting a particular lay length Xor by varying the lay length over a unit length of VR cable 200. Forexample, lay length X may be selected to increase damping in VR cable200 to dampen vibrations that may develop before the vibrations producedamage to VR cable 200 used in the power line.

Consistent with embodiments of the invention, the lay length may beoptimized. For example, the lay length may be optimized in order to havea range in a level of tightness between first conductor 205 and secondconductor 210. For example, if first conductor 205 and second conductor210 are twisted around one another too loosely, relative movementbetween first conductor 205 and second conductor 210 may be so greatthat bags may occur in cable 200. However, if first conductor 205 andsecond conductor 210 are twisted around one another too tightly,relative movement between first conductor 205 and second conductor 210may be so minimized that the aeolian vibration dampening effect in cable200 may be minimized to an undesirable level.

Consistent with embodiments of the invention, causing the power lineusing the vibration resistant cable to have a natural frequency notequal to an expected excitation frequency for an environment in whichthe power line is constructed may occur when the power line isconstructed to the minimum design conditions associated with theNational Electric Safety Code (NESC) standards. (See TABLE 2.)Furthermore the aforementioned bagging elimination and dampening effectfor vibration phenomenon may occur with the power lines built toNational Electric Safety Code (NESC) standards. Notwithstanding, theaforementioned desired attributes may occur with power lines constructedto any standard and is not limited to the NESC.

TABLE 2 NESC LOADING DISTRICTS Radial Ice Wind Design Thickness PressureConstants District Temp. (F.°) (inches) (psf) (lbs/ft) Heavy Loading  0°0.5 4 0.30 Medium Loading 15° 0.25 4 0.20 Light Loading 30° 0 9 0.05

In cable 200 first conductor 205 and second conductor 210 may be viewedas two coil springs that may be right beside each other. As cable 200 isstrung in the air between power line structures, sheaves holding cable200 at the power line structures may have a tendency to grab one of theconductors (e.g. first conductor 205 or second conductor 210.) Becauseof friction between first conductor 205 and or second conductor 210 andthe stringing sheaves, there is push back. If first conductor 205 andsecond conductor 210 are tight enough together as cable 200 tries topush back with a compressive, spring force, this force pushes back andprevents bagging. If may be assumed that friction between firstconductor 205 and second conductor 210 may be minimal (e.g. theconductors may be lubricated.)

The following equations show the relationship between first conductor205 and second conductor 210 in cable 200:

$\begin{matrix}{K = \frac{d^{4}G}{8D^{3}N}} & (1)\end{matrix}$

Where:

-   -   K is the spring rate    -   d is the diameter of the individual conductors    -   D is the distance between the two conductors    -   G is the modules of rigidity (a property like modulus of        elasticity)    -   N is the number of coils engaged or active coils        In the case that D and d are equal:

$\begin{matrix}{K = \frac{dG}{8N}} & (2)\end{matrix}$

Because (N)(LAY)=SPRING LENGTH,

$\begin{matrix}{N = \frac{SPRINGLENGTH}{LAY}} & (3)\end{matrix}$

Substituting (3) into (2)

$\begin{matrix}{K = \frac{(d)(G)({LAY})}{(8)\left( {{SPRING}\mspace{14mu} {LENGTH}} \right)}} & (4)\end{matrix}$

Locking force=(K) (deflection), then

${{Locking}\mspace{14mu} {force}} = \frac{(d)(G)({LAY})({deflection})}{(8)\left( {{SPRING}\mspace{14mu} {LENGTH}} \right)}$

-   -   for a cable with conductor diameter=d₁, Locking force is

${{{for}\mspace{14mu} d} = d_{1}},{{{Locking}\mspace{14mu} {force}} = \frac{\left( d_{1} \right)(G)\left( {Lay}_{1} \right)({deflection})}{(8)\left( {{Spring}\mspace{14mu} {Length}} \right)}}$Lay = Lay₁

-   -   for a cable with conductor diameter=d₂, Locking force is

${{{for}\mspace{14mu} d} = d_{2}},{{{Locking}\mspace{14mu} {force}} = \frac{\left( d_{2} \right)(G)\left( {Lay}_{2} \right)({deflection})}{(8)\left( {{Spring}\mspace{14mu} {Length}} \right)}}$Lay = Lay₂

For the same locking force for cable constructions with d₁ and d₂. Twodifferent cables:

$\begin{matrix}{\frac{d_{1}G\mspace{14mu} {Lay}_{1}{deflection}}{8\mspace{14mu} {Spring}\mspace{14mu} {Length}} = \frac{d_{2}G\mspace{14mu} {Lay}_{2}{deflection}}{8\mspace{14mu} {Spring}\mspace{14mu} {Length}}} & (5)\end{matrix}$

Now, setting (spring lengths) and (deflections) same for both cables,equation (5) reduces to:

$\frac{{Lay}\mspace{11mu} 1}{{Lay}\mspace{11mu} 2} = \frac{d_{2}}{d_{1}}$

As shown above, the change in “lay” to achieve the same locking forcewith the same deflection within the same active length of cable may belinear with the change in diameter “d”. This analysis neglects frictionin the model and assumes well lubricated conductors. Consequently, laylength changing with diameter of individual conductor element can createa “locking force” to prevent relative conductor sliding or movement.Movement prevention may stop bags or loops from forming while, forexample, making, installing, or using cable 200. A linear relationshipbased on the above formulas to describe the optimal lay of the cablewhich may prevent bags or loops, may be given as:

Lay=c ₁ d+c ₂,

-   -   where d is the conductor diameter and c₁ and c₂ are constants        that can be chosen to achieve the desired locking effect while        still providing enough relative movement in the cable for        effective Aeolian vibration dampening.        As described above, the locking force may minimize or prevent        conductor movement as described by the above equations that        relate to, for example, compression springs. Because first        conductor 205 and second conductor 210 become more spring-like        the shorter the lay length becomes, the spring forces in first        conductor 205 and second conductor 210 tend to prevent relative        movement of first conductor 205 and second conductor 210. In        other words, the shorter the lay length becomes, the more        resistant first conductor 205 and second conductor 210 becomes        to being either stretched or compressed. For example, the lay        length of VR cable 200 may be configured to cause a locking        force between first conductor 205 and second conductor 210        configured to prevent relative movement of first conductor 205        and second conductor 210 that would result in bags in VR cable        200 if the lay length were of a conventional length. The lay        length may be further configured to reduce a drag force when        wind blows across VR cable 200 when a component of the wind, for        example, is in a perpendicular direction to an axis of VR cable        200. For example, the drag force may be reduced by 2% to 3%.

FIG. 3A through FIG. 28 illustrate an operational example of cable 200that may show the effect of lay length on the stability of cable 200consistent with embodiments of the present invention. This operationalexample compares shorter lay VR cables or varying lay VR cables toconventional long lay cable. Consistent with embodiments of theinvention, a reduction in drag coefficient with shorter lay lengths maybe obtained as compared to conventional long lay cables. Consequently,consistent with embodiments of the invention, energy transferred intocable 200 may be reduced, which may reduce the likelihood of gallopingor vibration, for example. The same results may be applicable to icedcables as well.

As illustrated in FIG. 3A through FIG. 28, cables of varying lay lengthsmay be analyzed using Computational Fluid Dynamics (CFD) processes.Lift, drag, and moment on cables of fixed overall length (9 ft), butvarying lay lengths may be examined. Vortex shedding behavior is alsoexamined. Also, the effect of lay on the aerodynamic behavior of thecables is assessed. FIGS. 3A and 3B illustrate a “swallow” VR cable. Asshown in FIG. 3B, the cable comprises two individual conductors twistedtogether. Each individual conductors comprises of a total of sevenstrands, six 0.0937″ Al strands and one 0.0937″ steel strand (i.e.core.) The two conductors twisted together result in a cross-section ofthe VR cable as shown in FIG. 3B.

FIGS. 4A through 5B illustrate the VR cable's geometry. Athree-dimensional 9 ft. section is analyzed with respect to FIGS. 5Athrough 28. FIG. 4A shows a 3 ft. lay length, FIG. 4B shows a 9 ft. laylength, and FIG. 4C shows a combination 6 ft. and 3 ft. lay length.FIGS. 5A and 5B show a model depicting a mesh. FIG. 5A shows an overallmesh and FIG. 5B shows a close-up cable and mesh. In the flow model ofthe VR cable, a three-dimensional 9 ft. section is analyzed. FIG. 6A isa key for the directions. FIG. 6B shows the directions of the simulatedunsteady flow behavior of air at 25 mph over the VR cable.

Flow behavior may be analyzed by examining the behavior on planes (e.g.plane 1, plane 2, plane 2) of the VR lay configuration (geometry) ofFIG. 4A as shown in FIG. 7. FIGS. 8A, 8B, and 8C show flow velocity ofthe 3 ft. lay VR cable at plane 1, plane 2, and plane 3 respectively.FIGS. 9A, 9B, and 9C show pressure of the 3 ft. lay VR cable at plane 1,plane 2, and plane 3 respectively. FIGS. 10A, 10B, and 100 show flowvelocity at various times of the 3 ft. lay VR cable at plane 2. Velocity(m/s) on plane 2, as shown in FIGS. 10A, 10B, and 10C, at varioustime-instants indicates the time-dependent (e.g. chaotic) nature of flowbehavior. FIGS. 11A, 11B, and 11C show flow pressure at various times ofthe 3 ft. lay VR cable at plane 2. Pressure (Pa) on plane 2 at varioustime-instants indicates, as shown in FIGS. 11A, 11B, and 11C, thetime-dependent nature of flow behavior. FIGS. 12A, 12B, and 12C showforces on the 3 ft. lay VR cable at plane 1, plane 2, and plane 3respectively. To summarize the drag and lift of the VR lay configuration(geometry) of FIG. 4A (e.g. the 3 ft. lay), CFD computed an average dragforce on the 9 ft. cable (3 ft. lay), for example, is 1.92 N. The CFDcomputed movement and lift force on the 9 ft. cable (3 ft. lay), forexample, are negligible.

Flow behavior may be analyzed by examining the behavior on planes (e.g.plane 1, plane 2, plane 2) of the VR lay configuration (geometry) ofFIG. 4B as shown in FIG. 7. FIGS. 13A, 13B, and 13C show flow velocityof the 9 ft. lay VR cable at plane 1, plane 2, and plane 3 respectively.FIGS. 14A, 14B, and 14C show pressure of the 9 ft. lay VR cable at plane1, plane 2, and plane 3 respectively. FIGS. 15A, 15B, and 15C show flowvelocity at various times of the 9 ft. lay VR cable at plane 2. Velocity(m/s) on plane 2, as shown in FIGS. 15A, 15B, and 15C, at varioustime-instants indicates the time-dependent (e.g. chaotic) nature of flowbehavior. FIGS. 16A, 16B, and 16C show flow pressure at various times ofthe 9 ft. lay VR cable at plane 2. Pressure (Pa) on plane 2 at varioustime-instants indicates, as shown in FIGS. 16A, 16B, and 16C, thetime-dependent nature of flow behavior. FIGS. 17A, 17B, and 17C showforces on the 9 ft. lay VR cable at plane 1, plane 2, and plane 3respectively. To summarize the drag and lift of the VR lay configuration(geometry) of FIG. 4B (e.g. the 9 ft. lay), CFD computed an average dragforce on the 9 ft. cable (9 ft. lay), for example, is 2.011 N. The CFDcomputed movement and lift force on the 9 ft. cable (9 ft. lay), forexample, are negligible.

Flow behavior may be analyzed by examining the behavior on planes (e.g.plane 1, plane 2, plane 2) of the VR lay configuration (geometry) ofFIG. 4C as shown in FIG. 7. FIGS. 18A, 18B, and 18C show flow velocityof the 6 ft.-3 ft. combination lay VR cable at plane 1, plane 2, andplane 3 respectively. FIGS. 19A, 19B, and 19C show pressure of the 6ft.-3 ft. combination lay VR cable at plane 1, plane 2, and plane 3respectively. FIGS. 20A, 20B, and 20C show flow velocity at varioustimes of the 6 ft.-3 ft. combination lay VR cable at plane 2. Velocity(m/s) on plane 2, as shown in FIGS. 20A, 20B, and 20C, at varioustime-instants indicates the time-dependent (e.g. chaotic) nature of flowbehavior. FIGS. 21A, 21B, and 12C show flow pressure at various times ofthe 6 ft.-3 ft. combination lay VR cable at plane 2. Pressure (Pa) onplane 2 at various time-instants indicates, as shown in FIGS. 21A, 21B,and 21C, the time-dependent nature of flow behavior. FIGS. 22A, 22B, and22C show forces on the 6 ft.-3 ft. combination lay VR cable at plane 1,plane 2, and plane 3 respectively. To summarize the drag and lift of theVR lay configuration (geometry) of FIG. 4C (e.g. the 6 ft.-3 ft.combination lay), CFD computed an average drag force on the 9 ft. cable(6 ft.-3 ft. combination lay), for example, is 1.968 N. The CFD computedmovement and lift force on the 9 ft. cable (6 ft.-3 ft. combinationlay), for example, are negligible.

TABLE 3 below summarizes the above analysis on the VR cable consistentwith embodiments of the invention. As indicated in TABLE 3, the analysisindicates that the lifting force and torsional moment on the VR cablemay be negligible. The lay length may be no affect on this force and themoment. The lay length may have an effect on the drag force over the VRcable. A general trend where the drag force decreases with a decrease inlay length may be observed.

TABLE 3 Force (N) over 9 ft Cable Layout section of cable Comments 3 ft.lay cable 1.91 Lowest force of all cables analyzed 6 ft. and 3 ft. 1.97combination lay 9 ft. lay cable 2.01 Highest force of all 3 lay lengths

A distinct vortex shedding frequency may not observed for the VR cableas the angle of attack of the cable cross-section continuously changesalong the length of the VR cable. The forces computed using a 2danalysis compare reasonably with the 3d predictions. The drag forcepredicted using 3d simulations is lower than that predicted using 2dsimulations. As described below, the mechanism that leads to a reductionin the drag over the VR cable is explored by examining the details ofthe flow behavior over the cable.

FIGS. 23 and 24 show an examination of detailed flow behavior. FIG. 23shows the detailed examination for the 9 ft. lay VR cable (e.g. FIG. 4B)and FIG. 24 shows the detailed examination for a 3 ft. lay VR cable(e.g. FIG. 4A.) In FIGS. 23 and 24, span-wise flow is observed, whichmay lead to a reduction in the drag force.

Next, an examination of a detailed flow behavior for a 1 ft. lay VRcable will be shown. FIG. 25 illustrates a 3 ft. long section of a 1 ft.lay VR cable. To gain greater confidence in the trends observed using 3ft., 9 ft., and 3 ft.-6 ft. lay, a 1 ft. lay length cable isinvestigated. It is anticipated that a 1 ft. lay length cable will showmore dramatic results as compared to the other lay lengths. FIG. 26Ashows flow pressure at a times of the 1 ft. lay VR cable at mid spanplane. FIG. 26B is a corresponding force plot with respect to time.According to the examination, the drag force on the 3 ft. section of 1ft. lay length cable is 0.63N; this force is scaled to obtain the dragforce on a 9 ft. cable. The force on a 9 ft. long, 1 ft. lay lengthcable is (3*0.63) 1.89N. The lift force and moment on the cable arenegligible. FIGS. 27A and 27B show the examination of detailed flowbehavior for a 3 ft. lay VR cable. FIG. 27A shows velocity vectorsplotted near the surface of the 3 ft. lay VR cable. FIG. 27B showsvelocity vectors with span-wise speed.

As shown in TABLE 4 below, the CFD analysis predicts that the liftingforce and torsional moment on the VR cable may be negligible. The laylength may have no affect on the lift force and the moment. The laylength may have an effect on the drag force over the VR cable. A trendwhere the drag force decreases with a decrease in lay length may beobserved as shown in TABLE 4.

TABLE 4 Force (N) over 9 ft Cable Layout section of cable Comments 1 ft.lay cable 1.89 Lowest force of all cables analyzed (6% reduction in dragas compared to 9 ft. lay cable) 3 ft. lay cable 1.91 5% reduction indrag as compared to 9 ft. lay cable 6 ft. and 3 ft. 1.97 2% reduction indrag as combination lay compared to 9 ft. lay cable 9 ft. lay cable 2.01Highest force of all 4 lay lengths

Drag reduction over aerodynamic bodies may not easily achieved. A dragreduction of even 1-2% for aerodynamic shapes may be considered good. Adecrease in the net force acting on the VR cable may be observed with adecrease in lay length. A reduction in the net force on the VR cable andno change in the moment may result in a more stable cable. A closeexamination of the flow behavior may indicate span-wise flow along theVR cable. As illustrated in FIG. 28, the span-wise flow may be directedtowards the cross-section that subtends the smallest area to theincoming flow. The span-wise flow for the 1 ft. lay VR cable may behigher than that for the 3 ft. lay VR cable, which is higher than thatfor the 9 ft. lay VR cable. A trend indicating a decrease in drag withdecreased lay length may be observed. A preliminary assessment of theflow behavior may indicate that span-wise flow may be responsible for areduction in the drag force. This behavior may be similar to thatobserved for a swept aircraft wing. A backward sweep of the wing inducesspan-wise flow and a reduction in the drag and lift forces. VR cable layinduces twisting, which in turn may cause a span-wise flow to occur andhence a change in the drag force. Consequently, the above data indicatesthat the drag force over the VR cable may be reduced by reducing the laylength of the VR cable.

While certain embodiments of the invention have been described, otherembodiments may exist. Further, the disclosed methods' stages may bemodified in any manner, including by reordering stages and/or insertingor deleting stages, without departing from the invention. While thespecification includes examples, the invention's scope is indicated bythe following claims. Furthermore, while the specification has beendescribed in language specific to structural features and/ormethodological acts, the claims are not limited to the features or actsdescribed above. Rather, the specific features and acts described aboveare disclosed as example for embodiments of the invention.

1-30. (canceled)
 31. A vibration resistant cable comprising: a firstconductor having a diameter d; and a second conductor having thediameter d, the second conductor twisted around the first conductor at alay length between 3 feet and 6 feet to eliminate bagging of thevibration resistant cable during installation; wherein: the firstconductor comprises a plurality of first strands surrounding a firstcore strand, and the second conductor comprises a plurality of secondstrands surrounding a second core strand.
 32. The vibration resistantcable of claim 31, wherein the lay length is further configured to causea locking force between the first conductor and the second conductor toreduce relative movement.
 33. The vibration resistant cable of claim 31,wherein the lay length is further configured to allow some relativemovement between the first conductor and the second conductor to provideAeolian vibration dampening in the vibration resistant cable.
 34. Thevibration resistant cable of claim 31, wherein an optimum lay length isa function of the diameter d.
 35. The vibration resistant cable of claim31, wherein an optimum lay length is determined by the equation, c₁d+c₂,wherein c₁ and c₂ are constants configured to obtain a locking force toeliminate bagging in the vibration resistant cable and to provideAeolian vibration dampening in the vibration resistant cable.
 36. Thevibration resistant cable of claim 31, wherein the vibration resistantcable is not under tension in a power line.
 37. The vibration resistantcable of claim 31, wherein the lay length is varying.
 38. The vibrationresistant cable of claim 31, wherein the first conductor comprises sixfirst strands surrounding the first core strand.
 39. The vibrationresistant cable of claim 38, wherein the six first strands containaluminum, and the first core strand contains steel.
 40. The vibrationresistant cable of claim 31, wherein the second conductor comprises sixsecond strands surrounding the second core strand.
 41. The vibrationresistant cable of claim 40, wherein the six second strands containaluminum, and the second core strand contains steel.